LF Stability

[Terry Fox]

In looking at the information going back and forth regarding frequency
stability, I have a few comments.  Let me know if I am all wet.

1.  If we are going to communicate over long distances, we need some
method of determining what frequency to transmit, and therefore to
receive on.  The more accurate the two sides are on exact frequency, the
narrower the receiver can look.  This reduces noise, and can lead to
additional "processing gain".  The problem is how to coordinate the
frequency between the two sides to an amount that is worthwhile.

2.  Frequency stability is also an issue.  Both the transmitter and
receiver WILL drift.   They should either drift very. very slowly, or
one must track the other.  This drift can lead to one side drifting out
of the communications channel of the other, resulting in loss of
communications.

3.  Both of the above are important.  It is not good enough that the
receive LO is stable. Same with the transmitter.  It must also be
accurate, especially if a narrow-bandwidth receiver is used.  The above
is probably obvious, but should be kept in mind if we are to achieve
success.

4.  Milli-hertz reception using FFTs may be a good way of receiving
slowly modulated signals.  The problem is that it takes a finite amount
of time to collect the samples you will perform the FFT on.  As we
learned several years ago when we did the original Amrad FFT-based audio
spectrum analyzer on my 56001 DSP board, the hertz-per-bin is directly
related to the number of FFT points and sample rate.  If a signal is
sampled at 4000HZ, and a 1024-point FFT  is run, it will take 1024/4000,
or roughly 1/4 second to acquire enough samples to perform the FFT.
Nyquist says your maximum frequency is 2000Hz.  Since you only use the
real results, the FFT final product will be 1024/2, or 512 bins.  The
combination of the above yields a resolution-per-bin of about 2000/512,
or 4Hz (if I did my math right).  Bottom line is you will get number of
bins equal to half the number of FFT points.  Also, you must acquire
samples equal to the number of FFT points, before you can do the FFT.

As an example, if we want to do a 1024-point FFT, with a resolution of
0.1 Hz per bin, that means we need to collect roughly 1000 samples, as a
sampling rate of 100Hz.  It will take 10 seconds to collect these 1000
samples at 100Hz.  The numbers are not as clear using other FFT sample
rates, but the idea is the same.  Plently of processing time to do the
FFT, but the signalling speed must be very slow, or you will end up with
a bit symbol overlapping multiple FFT bins.  It still takes the inverse
of Hz/bin to get the number of samples to run the FFT (I think).

5.  I have been playing with building an LF receiver for the better part
of a year now.  One of the core pieces is that both LOs are based on
Analog Devices AD9832 DDS oscillilators.  To overcome both frequency
accuracy and frequency stability, I propose to periodically move the
receiver to a known reference signal (such as WWV with a small frequency
offset), and perform a large FFT.  Using the results of the FFT, actual
receive frequency can be calculated very accurately (much better than
aural or scope beating of frequencies).  The receiver is now calibrated
for a while, and can go back to the frequency of interest.  Since both
LOs are using the same master oscillator, and that oscillator error is
now known, we can assume accurate frequency operation.  If this is done
periodically, drift is also accounted for.  This approach does not rely
on yet another oscillator (or more), to verify accuracy.

6. I love the AD9832 DDS, and it's big brother the AD9850/51, and plan
to use them for lots of fun stuff.  It takes a 25MHz oscillator in, and
divides that by a 32-bit binary number, for an output from below 1HZ to
over 9MHz.  The down-size is that a low-pass filter is required on the
output, and the output impedance is 300ohm.  I have a 5-pole butterworth
filter and an AD817 op-amp buffering the output.  The AD9832 is
controlled by a 3-wire serial interface, which at the moment I drive
from a parallel port.  It can move to other frequencies instantly, based
on how fast you can load the 32 bits (or maybe less).  In addition,
there are two frequency registers, and 4 phase registers that modify the
output signal.  These are controllable from software, or hardware pins.
Can anyone say frequency hopping?  How about FSK or QPSK, or??   Neat
device.  I am making a small PC board for the device, that incorporates
the oscillator, 9832, and some biasing and bypassing parts.  The end
result is a 24-pin, .6 inch module that will plug into a 24-pin socket.

Well, that some ideas and comments for now.  Please comment back if I am
in error, or to amplify on above.  Terry, WB4JFI.